Journal
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume 278, Issue -, Pages 423-444Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2014.05.020
Keywords
Impact loading; Computational homogenization; Multi-scale model; Quasi-brittle materials; Representative volume element; Dispersion effect
Funding
- Netherlands Technology Foundation (STW) [10615]
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A dispersive multi-scale model is presented to model failure in heterogeneous quasi-brittle materials under high frequency loading conditions. In the dispersive multi-scale model, the heterogeneous model undergoing localized failure is replaced by a homogeneous macro-scale model with a cohesive crack and a meso-scale model with diffuse damage. Each material point of the macro-scale model is linked to a heterogeneous meso-scale model. The macro-crack is modeled as a strong discontinuity and the gradient-enhanced damage model is used to model diffuse damage in the meso-scale model. The constitutive law for the bulk material is obtained from the meso-scale model analysis using a standard computational homogenization scheme. The cohesive law for the macro-crack is obtained using a continuous discontinuous homogenization scheme which is based on a failure zone averaging technique. In the dispersive multi-scale model, at the macro-scale, a dynamic analysis is performed and the meso-scale model is solved as a quasi-static problem. The meso-scale inertia forces are taken into account via a dispersion tensor which only depends on the meso-scale model material properties and the heterogeneity of the material. The meso-scale inertia effects appear as additional body forces in the macro-scale model and cause dispersion of the propagating wave. The effect of dispersion on the cohesive cracking is captured via a rate dependent cohesive law. The dispersive multi-scale model is verified against a direct numerical simulation and the objectivity of the scheme with respect to the representative volume element size is shown. (C) 2014 Elsevier B.V. All rights reserved.
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